There are a few types of river surfing. One is the tidal bore surfing which happens when the Spring and Autumn tides are really high and the tidal surge travels up certain rivers. This surge creates a wave that can be surfed far inland. Sometimes for miles. The most famous tidal bores are on Severn river, Mascaret River and of course Amazon river.
Then there is the standing wave river surfing. A standing wave on a river is a wave that does not move. Strong river flow over an underwater obstacle can create a wave that can be surfed. The most famous standing river wave is in Munich, Germany. And it looks like this: